Cost-performance tradeoff in multi-hop aggregation for statistical inference

The problem of distributed fusion for binary hypothesis testing in a multihop network is considered. The sensor measurements are spatially correlated according to a Markov random field (MRF) under both the hypotheses. A fusion scheme for detection involves selection and localized processing of a subset of sensor measurements, fusion of these processed values to form a sufficient statistic, and its delivery to the fusion center. The goal is to find a fusion scheme that achieves optimal linear tradeoff between the total routing costs and the resulting detection error exponent at the fusion center. The Neyman-Pearson error exponent, under a fixed type-I bound, is shown to be the limit of the normalized sum of the Kullback-Leibler distances (KLD) over the maximal cliques of the MRF under some convergence conditions. It is shown that optimal fusion reduces to a prize- collecting Steiner tree (PCST) with the approximation factor preserved when the cliques of the MRF are disjoint. The PCST is found over an expanded communication graph with virtual nodes added for each non-trivial maximal clique of the MRF and their KLD assigned as the node penalty.